|
Young Researchers Workshop: Kinetic and macroscopic models for complex systems
|
Contagion shocks in one dimension
Li Wang
University of California, Los Angeles
|
Abstract:
Contagion models involve emotional states that affect individuals?
behavior. We consider an agent-based contagion motion model in one dimension that has recently been studied in the artificial intelligence community. The model involves movement proportional to a "fear" variable which undergoes a temporal consensus averaging based on distance to other agents. We consider "Riemann initial data" for this problem corresponding to shock dynamics in a continuum limit. We consider distinguished limits as the contagion interaction distance and the interaction timescale vanishes. The limiting behavior is related to a classical model for pressureless gas dynamics with "sticky" particles. In comparison we observe a threshold for the interaction distance vs. interaction timescale that produce qualitatively different behavior for the system - in one case particle paths do not cross and there is a natural Eulerian limit involving nonlocal interactions and in the other case particle paths can cross and one may consider only a kinetic model in the continuum limit. |
|